It has been a problem to provide accurate positioning and holding the electrodes of an electroencephalographic apparatus in operative contact with a patient's scalp without inducing a muscular reaction that interferes with brain potentials of interest. Activity of the facial or neck muscles produces electrical voltages or potentials that add to the potentials appearing on the scalp as a result of brain activity and thus produce false or interfering signals. To position the electrodes it has been proposed to mount the electrodes in a rigid helmet-like cap that is placed on the patient's head. This is unsatisfactory because of the variations in skull shape and size from patient to patient and the difficulty of getting uniform pressure on the various electrodes. The misfits usually resulted in patient discomfort and muscular reactions. It has also been proposed to use a flexible cap arrangement with a hold down strap under the patient's chin or lower jaw. If the strap is tight enough to hold the cap and electrodes firmly in place it is annoying to the patient and induces a muscular reaction in the facial and jaw muscles and thus unwanted or interfering electrical potentials.